You never know this can just be simulation by that " hovering superintelligence " and it is so powerful that it can create complete accurate virtual characters.
Hey 3blue1brown, I recently saw a math problem that I think you could give a neat explanation to. It goes like this: “Pick x,y uniformly form (0,1). What is the probability that x/y rounds to an even number?” I’d love to get a good intuitive argument for why pi shows up in the answer (I trust the math but it comes out of nowhere).
pi? When I work it out I get (1 - ln(2) / 2) as the answer, which also lines up with the numerical experiments I did. Are you have the right puzzle/answer pairing? It was a lovely puzzle, thanks for sharing, I may very well make a quick video on it at some point.
Okay, yes, it looks like the answer (5 - pi) / 4. That's very pretty. It comes from first looking at the unit square representing pairs (x, y), then slicing it into regions that look like (n/2) * y < x < ((n + 2)/2) * y for odd n. The presence of pi stems from Leibnitz formula, that pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ....
You totally earned 2^21 subscribers! A math student who doesn't love your videos probably studies the wrong subject. Much love from Germany! It's true that if someone doesn't seem to know you at least 2 people will shout out "How can you not know 3blue1brown?"
"no matter what you do, your kids are gonna do things just like you" remember. be curious, i guess.. that is like a seed to grow a whole forest. don't teach the content, teach the pattern that unlocks all these different kinds of contents and applications. everyone who is good at a subject, is passionate about something. be passionate and your kids will see how to be just that. it's a metaskill contentwise
You seem too young, I had imagined much mature mid-aged person given the deep voice and domain knowledge. My mind still feels a young man lip-synced to the voice.
His voice isn't deep, but it's definitely rich and slow. The kind of voice that sounds like it should have taken much more experience than 27 years can give.
@@subaruyagami2327 Audio engineer here: shrillness is usually due to the frequency spectrum of the voice, not the pitch or fundamental frequency. A sine wave at 1kHz is not shrill (think of a high pitched whistle), but a 90-10 pulse-width waveform at 1kHz is, because there's a build-up of harmonics at frequencies the human ear is very sensitive to (1-10kHz).
Applied math is far superior to theoretical math for introducing people with less experience to new concepts, because learning works by forming connections to things you already understand. However, if you've studied enough math, then you can start doing theoretical math and using your prior math knowledge as the thing you already understand. The only thing to avoid is becoming so engrossed in the theoretical that you can no longer relate fascinating new ideas back to reality in some way. I believe this applies to essentially all things, not just math. Music theory vs. playing with instruments. Computer science vs. writing code. Color theory vs. pottery. All practices have some theory and some pragmatism, and you can either focus on one side of things, or dive just far enough into both to find a happy middle ground where you can have the best of both worlds.
dandymcgee - This is actually how I got to know this channel! I was studying audio editing, and I had to learn a lot about mathematical concepts that can be applied on signals, like the Fourier Transformation for an example.
@@Schattengewaechs99 I came from an audio background too, so it's cool to see someone else did. Out of interest, how come you needed to know about the FFT for audio editing? Is it for a course you're taking or was it out of curiosity? I write realtime audio software (VST plugins), and would happily help you out. Learning about the z-Transform is what really made things click for me regarding the DFT, and I have some great accessible resources to share if you're interested.
damn, this does sound like a trap i fallen into, i was way too into math of music, how sound is actually made, making patches in softsynth was my favorite pastime. and now i barely make any music at all. in all honesty i subbed to this channel because it was talking a lot about FFT, something i sort of "worship", as visualization of sound helped me so much to understand and "see" it. eventually i realized it was counter intuitive, and in a lot of ways was a crutch, relying too much on eyes than ears.. and forgetting that music was about creativity... not math
@50 u gotta go do some more basic applied math first, if you're trying to do applied math at the same level as your pure math it's not going to be good for learning. i'm studying maths and physics and i've found that just doing physics problems alongside the standard 1st-2nd year math made me good at applied. i've had good success taking a pure and applied perspective on any applied math problems, it took me a few years to really develop it (2-3), but it has been so useful as a mindset. Ex. GF(2) is both interesting from a pure and applied perspectives. Pure: smallest finite field of {0,1}. Applied: has addition equivalent to XOR and multiplication equivalent to AND. it's super useful in information theory from the lil bit i learnt.
First time I've ever felt compelled to comment on anything: thank you for addressing the anxiety/depression/adhd question. It took me off guard to see it come up on your channel (which I subscribe to partially as a treatment for all those conditions). I can't imagine it being answered better. Your calm, modest brilliance is what the world needs right now. Thank you!
Claude Shannon, a man who loved the pairing of the curiously useless to the absolutely crucial. One of the only people to formulate, substantially develop, and write the seminal paper on one of the most important theories in history. Simply unbelievable.
For fathers: don’t just pay attention to something to indicate its importance. Involve your kid to make it enticing. If you focus on something in an exclusive way, it won’t necessarily spark interest rather than resentment. IMO
I am into video games, and I'm a self-taught programmer, as well as a (mainly) self-taught mathematician. And I absolutely adore your videos and your explanations! You... are... amazing! You've helped me a lot! You're intuitive and you should keep this going, because MANY people need just that in order to compensate for a bad/insufficient education system. The work and the results you've achieved while popularizing math is just amazing.
Great comment. But, he's not referring to any (imminent) child of HIS, but rather the child of the questioner. Fun fact to make you feel better about that confusion: His own mother watching this video got faked raw by this very same misunderstanding and believed she had just learned of her first grandchild's conception. (And no, I'm not kidding)
I am so glad I discovered your channel. There are many excellent math channels on TH-cam that I have grown fond of, and yours is my favorite. You are really great at expressing things in intuitive ways, and you know how to teach such that the person being taught is engaged, rather than simply vomiting out a bunch of information and hoping the listener magically absorbs it like some conceptual sponge. Your animations are extremely helpful, too. In school, much of what we were taught was done so via spoken sentences, and other linear ways of going about things. While that has its place, it just can't compete with the potential that something like a visual can convey. It also helps make the mathematics alive, artistic, and creative, as opposed to memorizing formulas, for example. You have videos 10-20 minutes long that have been more effective for me than - in many cases - multiple weeks in school. Even though I always did really well in my math classes, upon watching some of your videos, I can see in hindsight that I didn't have as solid of a grasp on many concepts as would have been suggested by my test scores. I have subscribed and look forward to many more of your videos! I really enjoyed getting to hear from you about things not directly related to mathematics. You are clearly very intelligent, but more importantly than that, you have some mysterious quality that I don't often encounter and don't know how to describe... perhaps later I will find the words. Also, I have discovered some mathematical patterns throughout my life that, as far as I know, have never been discussed before. I would love to describe them to you and see if you can figure out what underlies them. If you're willing, I will reply back with what they are.
Math is like a violin. There are great violin makers and great violin players; but rarely if ever has the greatest creator of violins been the greatest writer of songs and the greatest performer. For a violin to have value, there must be music, musicians and---of course---a violin maker. The one time I watched a man (on TH-cam) play a piece he had written on a violin he had made, I felt like I was witnessing something a little different than ever before. Not necessarily great, but different. Even the most pure mathematician needs the symbols created first by people trying to reconstruct the world they heard, saw and touched.
@@jajefan123456789 Since the hallmark of math is precision of language (as much as possible), I changed the 2nd 'song' to piece. The 1st use of song just did not resonate as 'piece.' Thank you for the correction.
I've gotta say, I love your voice. Its very relaxing and there has been times that when I can't sleep I just put Essence of Calculus on autoplay and listen to your voice.
I just wanted to thank you for everything! You really work hard to explain things to us. Personally you’ve changed the way I’ve perceived mathematics and for that I’m grateful!
It is incredible how many subs you have gained. Good indicator of how many people prefer intuitive math videos rather than boring vids that don't explain why those topics are interesting or even where do they come from.
I’m a 17 year old high school student and I’m going to uni next year. I’ve got a profound passion for computer science and cryptography, however I also really love maths and most of the famous cryptographers were obviously mathematicians so I was in a bit of a dilemma which study to choose. But thanks to your little talk on “mathematician + x” I’ve now definitely decided to go study technical computer science and learn all the left over maths by myself if I have to. Thanks!
Why not double-major? You may be able to study both at the same time. That's what I did and even though it's a lot of work, it is worth it for someone with your interests. Many computer science people don't have the strongest math skills, and few math people have strong computer science or programming. Having both becomes very useful, especially if you want to study cryptography which spans both worlds.
I double majored in both, and while I don't use the pure mathematics from undergrad (I'm currently a software engineer), the problem solving skills and techniques for abstracting problems have been incredibly useful.
I avoid math majors because teachers in my country never seems to have interest in teaching math. From middle to high school, so college must be that way too. All they taught is to "Remember the Magic Algorithm of Math Formulas", i've had enough of that shit ever since i finally learn from internet that it's the wrong way to learn math.
Good choice. You don’t need math courses to learn math. I even believe self-study math is way better. Math lecture is like definition-theorem-proof. You don’t have time to think it first yourself. But self-study is very different. Sure listening to lecture is easier, but it’s worth to spend the extra time to tackle it yourself. Also, undergraduate math course often goes extremely slow.
Hey 3blue1brown! As a current Mathematics Major, I absolutely love watching your video! You have s really deep intuition in terms of math or anything that is physics related! Dont stop making videos! >=
As an engineering student, I won't be taking any more further studies into math past basic discrete mathematics and some basic levels of vector calculus. Your channel is there to keep me interested in the subject and act as a way to show me the true beauty behind the world of mathematics on an intuitive level. Thank you so much for your work.
Haha what a coincidence I just learned Stokes theorem in calc 3. It's funny what my professor told me, apparently Stokes was a professor at Cambridge and he made a problem for PhD students which was basically proving Greene's theorem in 3d
8:34 Here's a Mental health PSA/personal story. There are three decisions in my life I regret not making sooner. I wish I had broken up with an abusive ex earlier, I wish I had dropped out of college earlier, and I wish I had addressed my mental health earlier. I'm now in a happy 4-year relationship, planning financially to go back to finish my degree in a year or two, and seeing a psychiatrist and therapist regularly. It is not weak to seek help. On the contrary, it is one of the bravest things you can do. Things will not stay bad forever. It may take a long time to realize how much progress you're making, but it will happen.
I love studying engineering and hearing " Shannon " in my control systems lectures about sampling, and then in this video 🤔 it really gives perspective
I marvel at your resolve to communicate mathematics in an interesting and enjoyable way. I have been a mathematician for over 30 years now, and I always take something new away from watching your videos. Thank you!
Totally agree with your point on "how to turn someone on to maths". I used to not particularly enjoy maths until I felt like I really needed them as a software developer. I finally got around to learning about vector geometry and linear algebra one day and it opened up a whole new world of possibilities for me as a programmer and I felt like it sharpened my "logical mind" if that makes sense. From then, I was hooked.
THAT'S SOOOOO TRUE!!! WHEN YOU KNOW HOW POWERFUL IT IS, HOW IT CAN TURN SOMETHING SEEMINGLY SO COMPLEX INTO SOMETHING MORE APPROACHABLE, MORE UNDERSTANDABLE, YOU CAN'T HELP FALLING FOR IT!!! WELL SAID!!
I don't know if anybody ever told you that: your voice is absolutely great; it's a pleasure to listen to your videos. Which is to mean that your videos are phantastic anyway, but the sound of your voice just makes them even more enjoyable.
God it's so exciting watching him explaining things. Grant is a genius. I dunno why but I burst into tears when he compares the reference material with pedagogical material. What a brilliant theory!
TLDR: necessity is the mother of invention Being a 'Mathematician + X' has certain unique benefits which make it my preference. Being an X is important for fundamental and initial research in any area. For example, nowadays it's normal to talk about n-dimensions but the person who initially thought about representing "dimension" through a line and locating specific places on it ( points) must have started out with just one dimension in mind. The question now becomes why did they feel the need to think about the world in such a manner. This is where the X comes in. Being that X is maybe what necessitates thinking about these problems in a new way. Maybe the person being talked about was involved in trade and needed a way of measurement. Although I agree not every example will abide by this POV but a surprising number of them will.
Or you could try writing a software that'll detect the camera shake, and then program a mechanical stabilizer to cancel it out for you. Works every time. Try it!
I am just studying information theory for my EE degree and when you named Shannon as one of your favorite mathematicians I was so happy. I also love information theory, it is a real shame not many people know about this topic.
7:27 This is so real. I switched to the math major because I thought it would be the easiest major to switch to that would lead me to a job without going to grad school. Growing up, I thought math was boring and easy, but I ended up falling in love with it and will be pursuing a PhD in the fall
Applied Math. Two-year-olds or thereabouts have been watching others open and close doors and drawers by pulling and pushing on knobs and handles. For days and weeks and months they struggle to learn the secrets and perfect their processes of opening and closing doors and drawers by pulling and pushing and turning every which way on knobs and handles and changing their trials and techniques as they observe the fruits of their labor. Adults may see their efforts as play or mischief, but their brain is learning a form of applied math that only a small number of physics or engineering graduate students may study and understand. Suppose that your task is to move some object or articulating mechanism in some way using your finger(s) and/or hand(s). In a few seconds you analyze the object or mechanism and then apply your finger(s) and/or hand(s) to it in some way(s) and expect to see resulting movement(s). You evaluate the result(s) as feedback and may adjust your finger(s) and/or hand(s) input(s) to change the observed result(s). Our brains are quantifying what may be referred to as mechanism mobility associated with specific spatial directions. Suppose you want to open a closed door using a rotatable knob. Your brain believes that your hand must turn the knob left or right to release an internal latch and then your hand must pull or push on the knob in a direction perpendicular to the door's surface. Your brain believes that these may be the best directions because experience has shown that they generally offer higher mobility. Your brain is also aware of other directions of lower to zero mobility, which it believes would take much higher levels of effort to open the door, if at all. So it avoids them or may eventually try some as a last-ditch effort if all else has failed. My future applied math challenge will be to describe a numerical methodology that will provide quantitative/qualitative assessment(s) of mechanism mobility, similar to what our brains are doing with very little effort on our part.
Wow it's so amazing to finaly see the face behind the voice. Your explantions are very coharentic, with a great graphic demo and a calm tone. I send you from Israel my BIG FAT LIKE!
@@moartems5076 nearly all physics in simple engines is frame-based iterative summing of the velocity and position, then some comparisons to do collision. Even computing collision time is a closed-form quadratic equation in most cases. I've seen some suggestion that partial derivates are needed to handle things like cloth simulation reasonably, because energy conservation is really important there, but otherwise the systems tend to be too dynamical for inaccuracies to matter much. What has your experience been?
@@moartems5076 Eh. I see the point you're trying to make, but the actual math knowledge required is primary school level. You're probably not really doing numerical analysis here until you're doing something like computing error bounds from the exact solution, eg. to figure out physics update rate lower bounds.
I think he should make more videos where he shows himself. I loved the numberphile video featuring him about the hyper-darts problem. I highly recommend it!
@@thedoublehelix5661 Well, maybe you're right but I really like how Brady interacts with his guest mathematicians and how he makes some appreciations that would have been averted otherwise like when he asked about what happens with the center or the perimeter.
Sir, I really love the work you're doing. I love how you addressed the question of mental health because I've been spending a lot of time in the internet. Now I'll change my routine. Thank you so much for this Q&A. I would like you to do these kinds of videos every month. :)
"The Information" by Gleick is a masterpiece. I reread it every couple of years. Exactly how humans gained mastery (drastically decreasing entropy) by "learning" 🙂 to control information. Add a book on the evolution of RNA and metabolism (in the ocean) and the big picture comes into focus.
Disagree! Most people are not able to grasp advanced math. They are able to learn arithmetic but many start to fail when algebra is coming up in class already. I know that i cant. Its not the teaching method.
@@Steuben1978 I don't think so, because whenever people asked questions in class the teacher would shame that person. I was able to learn algebra with a better teacher outside of school, and Kahn academy has amazing lessons on there website. I agree that people form put in effort to understand concepts well enough, but the school systems also promote plug and play mathematics, they don't answer why we do it a certain way, they just give formulas and you put in number and answer them
Being very good at arithmetic is not a prerequisite for maths. They are two different subjects. In fact algebra is far easier than arithmetic if it is taught correctly. Teachers are not mathematicians and generally work as teachers because they are not experts in any subject (not all of them, but most of them). That is what is wrong with schools. If you selected the best teachers, then maths teaching at schools would work. But that is not how it is done.
@@kevinmccallister7647 That does not refute my point! People differ greatly in their intellectual ability. Yes, a bad teacher or a dysfunctional family can make things worse, but for the many people who lack the necessary spatial reasoning or mathmatical ability or have bad pattern recognition....even a good teacher will not be able to make them grasp advanced math.
What an interesting perspective, on why individual authors help people to get a foothold, by explaining it 'wrong' first. This is why experts in a field have so much difficulty simplifying an introductory lecture....
@Suki Desu People who don't like math should not be viewing this video. I believe that if you don't like a video on TH-cam, you should just move on. There's no need to be negative.
Since Terence Tao needed less than two hours to find three independent proofs of an identity about neutrino oscillations given by Stephen Parke, Xining Zhang, and Peter Denton, will they now rename the tau neutrino as Tao neutrino?
![ทุกครั้งที่หลับตา (Lucid Dream) - AYLA's [ Official MV ]](http://i.ytimg.com/vi/4i1OBAQyv58/mqdefault.jpg)
So, the voice actualy has a body, it is not a hovering superintelligence with a superb graphical interface?
Marcus Brühl strange he looks kinda like Vision from Marvel
You never know this can just be simulation by that " hovering superintelligence " and it is so powerful that it can create complete accurate virtual characters.
@@zotac1018 I HIGHLY believe we're living in a simulation honestly
@@estehbread What makes you say that?
@@codyk2573 I'm too dumb for this... ELI5 please?
Given the expression and background, I legit thought this was a Tom Scott video from the thumbnail :)
Was your second thought: "Where is the red shirt?"
Came to say this. Looks like a young Tom.
Its young american tom scott
Conor Kosidowski
Too short hair 😉
Me too, I was wondering why his hair was so short.
My mind is having severe problems matching that face with that voice.
I pictured him 10 years older with a beard.
I pictured him black
I thought he was beyond physical form.
@@naders.171 😂😂😂😂
@@StutiRajguru do i know you?
Picture this: You're going for a hike and walk past a man talking to his camera about bizarre mathematicians
If I heard this voice talking about maths I'd stop and listen.
@@0-Kirby-0 yes definitely
Normal in the Berkeley hills
You're walking in the woods. There's no one around and your phone is dead
Suddenly out of the corner of your eye you spot him
3blue1brown
this is a comment that I found funny and I'm not a mathematician actually I still feel very stressed about math and other school work. xD
That moment when you realize the spirit of math itself has a human form
Nice amount of likes
And a rather good looking one 😆
Hey 3blue1brown, I recently saw a math problem that I think you could give a neat explanation to. It goes like this:
“Pick x,y uniformly form (0,1). What is the probability that x/y rounds to an even number?”
I’d love to get a good intuitive argument for why pi shows up in the answer (I trust the math but it comes out of nowhere).
just commenting this so that I can be notified for any updates😅
Woah!
pi? When I work it out I get (1 - ln(2) / 2) as the answer, which also lines up with the numerical experiments I did. Are you have the right puzzle/answer pairing?
It was a lovely puzzle, thanks for sharing, I may very well make a quick video on it at some point.
Oh wait, I'm just doing this for rounding down (i.e. the floor function). Is the puzzle rounding to the closest integer?
Okay, yes, it looks like the answer (5 - pi) / 4. That's very pretty.
It comes from first looking at the unit square representing pairs (x, y), then slicing it into regions that look like (n/2) * y < x < ((n + 2)/2) * y for odd n. The presence of pi stems from Leibnitz formula, that pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ....
I didn’t realize I needed Grant saying “oh hunny, he’s not gonna change” until now
ា 16:07
Makes my day, everyday!💗
You totally earned 2^21 subscribers! A math student who doesn't love your videos probably studies the wrong subject. Much love from Germany! It's true that if someone doesn't seem to know you at least 2 people will shout out "How can you not know 3blue1brown?"
Thanks so much!
"no matter what you do, your kids are gonna do things just like you"
remember. be curious, i guess..
that is like a seed to grow a whole forest.
don't teach the content, teach the pattern that unlocks all these different kinds of contents and applications.
everyone who is good at a subject, is passionate about something.
be passionate and your kids will see how to be just that.
it's a metaskill contentwise
Check your grammar.
Definitely one of the best comments I've read for a while..
Nice 1...
I should add that I don't even have kids...
Anyone with kids knows this is completely wrong
@@EdwardT9 do you have kids
You seem too young, I had imagined much mature mid-aged person given the deep voice and domain knowledge. My mind still feels a young man lip-synced to the voice.
He doesn't have a deep voice at all 😐
Outside yeAh I don’t find his voice deep if anything I find it high pitch at times
His voice isn't deep, but it's definitely rich and slow. The kind of voice that sounds like it should have taken much more experience than 27 years can give.
@@alexandria5758 high pitch voice is very shrill, which his voice clearly isn't.
@@subaruyagami2327 Audio engineer here: shrillness is usually due to the frequency spectrum of the voice, not the pitch or fundamental frequency. A sine wave at 1kHz is not shrill (think of a high pitched whistle), but a 90-10 pulse-width waveform at 1kHz is, because there's a build-up of harmonics at frequencies the human ear is very sensitive to (1-10kHz).
Applied math is far superior to theoretical math for introducing people with less experience to new concepts, because learning works by forming connections to things you already understand. However, if you've studied enough math, then you can start doing theoretical math and using your prior math knowledge as the thing you already understand. The only thing to avoid is becoming so engrossed in the theoretical that you can no longer relate fascinating new ideas back to reality in some way.
I believe this applies to essentially all things, not just math. Music theory vs. playing with instruments. Computer science vs. writing code. Color theory vs. pottery. All practices have some theory and some pragmatism, and you can either focus on one side of things, or dive just far enough into both to find a happy middle ground where you can have the best of both worlds.
dandymcgee - This is actually how I got to know this channel!
I was studying audio editing, and I had to learn a lot about mathematical concepts that can be applied on signals, like the Fourier Transformation for an example.
@@Schattengewaechs99 I came from an audio background too, so it's cool to see someone else did. Out of interest, how come you needed to know about the FFT for audio editing? Is it for a course you're taking or was it out of curiosity?
I write realtime audio software (VST plugins), and would happily help you out. Learning about the z-Transform is what really made things click for me regarding the DFT, and I have some great accessible resources to share if you're interested.
damn, this does sound like a trap i fallen into, i was way too into math of music, how sound is actually made, making patches in softsynth was my favorite pastime. and now i barely make any music at all. in all honesty i subbed to this channel because it was talking a lot about FFT, something i sort of "worship", as visualization of sound helped me so much to understand and "see" it. eventually i realized it was counter intuitive, and in a lot of ways was a crutch, relying too much on eyes than ears.. and forgetting that music was about creativity... not math
@50 u gotta go do some more basic applied math first, if you're trying to do applied math at the same level as your pure math it's not going to be good for learning. i'm studying maths and physics and i've found that just doing physics problems alongside the standard 1st-2nd year math made me good at applied. i've had good success taking a pure and applied perspective on any applied math problems, it took me a few years to really develop it (2-3), but it has been so useful as a mindset. Ex. GF(2) is both interesting from a pure and applied perspectives. Pure: smallest finite field of {0,1}. Applied: has addition equivalent to XOR and multiplication equivalent to AND. it's super useful in information theory from the lil bit i learnt.
Such a good comment! As a musician I truly agree with you, and also find math interesting
First time I've ever felt compelled to comment on anything: thank you for addressing the anxiety/depression/adhd question. It took me off guard to see it come up on your channel (which I subscribe to partially as a treatment for all those conditions). I can't imagine it being answered better. Your calm, modest brilliance is what the world needs right now. Thank you!
It's said that by the time he finished recording this vlog, he was somewhere in Venezuela.
😂😂
Top comment. 😂😂😂
Awesome achievement. Not many hikers have made it across the Darien Gap!
Can someone please help me out with this: simplify (1+1/a)(1+1/a^2)(1+1/a^4)...(1+1/a^1024)
@@anshum1675 I believe it can be rewritten as: ... = (capital pi: n = 1 -> 512) (1+1/a^(2n))
"Within two hours he found three independent proofs of this thing"
Such a Terry Tau thing to do
Oh look they used the de-aging tech on Tom Scott.
Tom Scott was long-haired brown-haired guy, he has videos 8 years ago on youtube. His hair only became white, he's actually still young.
he looks like Tom Scott with a hint of Conan O'Brien
@@Ultiminati Still almost 10 years older than Grant
@@windingsarcasm9046 I mean, Tom’s only 36, do you think Grant is 26 or under?
Claude Shannon, a man who loved the pairing of the curiously useless to the absolutely crucial. One of the only people to formulate, substantially develop, and write the seminal paper on one of the most important theories in history.
Simply unbelievable.
Honestly, I thought this was awesome! Very conversational in style and quite enjoyable.
For fathers: don’t just pay attention to something to indicate its importance. Involve your kid to make it enticing. If you focus on something in an exclusive way, it won’t necessarily spark interest rather than resentment. IMO
Mothers too imho
Yep. My dad spends a ton of time making music for fun but I never became interested since he does it all on his own.
Tell me why he reminds me of what a young Conan O’Brian would look like.
His smile is so very similar to Tom Scott's
just without the arrogance
@Morten Holst Maybe he was referring to Conan and not Tom?
The hair
Can someone please help me out with this: simplify (1+1/a)(1+1/a^2)(1+1/a^4)...(1+1/a^1024)
i wanna be this guy's friend, damn hes interesting.
@Sree Veda Become intersting yourself ?
I am into video games, and I'm a self-taught programmer, as well as a (mainly) self-taught mathematician. And I absolutely adore your videos and your explanations! You... are... amazing! You've helped me a lot! You're intuitive and you should keep this going, because MANY people need just that in order to compensate for a bad/insufficient education system. The work and the results you've achieved while popularizing math is just amazing.
Great comment. But, he's not referring to any (imminent) child of HIS, but rather the child of the questioner. Fun fact to make you feel better about that confusion: His own mother watching this video got faked raw by this very same misunderstanding and believed she had just learned of her first grandchild's conception. (And no, I'm not kidding)
@@piman7319 Haha, seriously? I might have been tired and misheard :D Sorry about that. I edited my comment in order to spare the confusion.
I am so glad I discovered your channel. There are many excellent math channels on TH-cam that I have grown fond of, and yours is my favorite. You are really great at expressing things in intuitive ways, and you know how to teach such that the person being taught is engaged, rather than simply vomiting out a bunch of information and hoping the listener magically absorbs it like some conceptual sponge.
Your animations are extremely helpful, too. In school, much of what we were taught was done so via spoken sentences, and other linear ways of going about things. While that has its place, it just can't compete with the potential that something like a visual can convey. It also helps make the mathematics alive, artistic, and creative, as opposed to memorizing formulas, for example.
You have videos 10-20 minutes long that have been more effective for me than - in many cases - multiple weeks in school. Even though I always did really well in my math classes, upon watching some of your videos, I can see in hindsight that I didn't have as solid of a grasp on many concepts as would have been suggested by my test scores.
I have subscribed and look forward to many more of your videos!
I really enjoyed getting to hear from you about things not directly related to mathematics. You are clearly very intelligent, but more importantly than that, you have some mysterious quality that I don't often encounter and don't know how to describe... perhaps later I will find the words.
Also, I have discovered some mathematical patterns throughout my life that, as far as I know, have never been discussed before. I would love to describe them to you and see if you can figure out what underlies them. If you're willing, I will reply back with what they are.
mine too
im gonna say it
grant is cute
tomdrug imma say it
i 100% agree
Also his voice is soothing as hell
He's a snacc
omg me too, he's so cute when he is talking about math
Ikr! He is so cute and young and intelligent... I adore him🥺
Math is like a violin. There are great violin makers and great violin players; but rarely if ever has the greatest creator of violins been the greatest writer of songs and the greatest performer.
For a violin to have value, there must be music, musicians and---of course---a violin maker.
The one time I watched a man (on TH-cam) play a piece he had written on a violin he had made, I felt like I was witnessing something a little different than ever before. Not necessarily great, but different.
Even the most pure mathematician needs the symbols created first by people trying to reconstruct the world they heard, saw and touched.
Fran Tabor small clarification: songs are sung, while pieces are played. Otherwise, great analogy!
@@jajefan123456789 Since the hallmark of math is precision of language (as much as possible), I changed the 2nd 'song' to piece. The 1st use of song just did not resonate as 'piece.' Thank you for the correction.
For some reason, I always pictured 3Blue1Brown as a bald guy.
He face revealed sometimes b4, so it was no new thing for me
With thick rimmed spectacles.
I thought he was an Indian dude
Mathologer
Mathologer reference
I just can't wait, to see it, I wait for every 3blue1brown's video ❤️😃
I've gotta say, I love your voice. Its very relaxing and there has been times that when I can't sleep I just put Essence of Calculus on autoplay and listen to your voice.
Excellent teacher- Explains the Forest while admiring , and not minimizing the Trees
Itd be cool to have a series "the essence of topology" where he explains the big concepts such that connectness, compactness etc
Thank you for caring about us! Love this channel!
This guy is literally 'math' just walking around as a human
I just wanted to thank you for everything! You really work hard to explain things to us. Personally you’ve changed the way I’ve perceived mathematics and for that I’m grateful!
this was just lovely.
It is incredible how many subs you have gained. Good indicator of how
many people prefer intuitive math videos rather than boring vids that
don't explain why those topics are interesting or even where do they
come from.
Gonna tell my kids: he's (grant) best mathematics teacher I ever had.
I’m a 17 year old high school student and I’m going to uni next year. I’ve got a profound passion for computer science and cryptography, however I also really love maths and most of the famous cryptographers were obviously mathematicians so I was in a bit of a dilemma which study to choose. But thanks to your little talk on “mathematician + x” I’ve now definitely decided to go study technical computer science and learn all the left over maths by myself if I have to. Thanks!
Why not double-major? You may be able to study both at the same time. That's what I did and even though it's a lot of work, it is worth it for someone with your interests. Many computer science people don't have the strongest math skills, and few math people have strong computer science or programming. Having both becomes very useful, especially if you want to study cryptography which spans both worlds.
I double majored in both, and while I don't use the pure mathematics from undergrad (I'm currently a software engineer), the problem solving skills and techniques for abstracting problems have been incredibly useful.
I avoid math majors because teachers in my country never seems to have interest in teaching math. From middle to high school, so college must be that way too. All they taught is to "Remember the Magic Algorithm of Math Formulas", i've had enough of that shit ever since i finally learn from internet that it's the wrong way to learn math.
Good choice. You don’t need math courses to learn math. I even believe self-study math is way better. Math lecture is like definition-theorem-proof. You don’t have time to think it first yourself. But self-study is very different. Sure listening to lecture is easier, but it’s worth to spend the extra time to tackle it yourself. Also, undergraduate math course often goes extremely slow.
Hey 3blue1brown! As a current Mathematics Major, I absolutely love watching your video! You have s really deep intuition in terms of math or anything that is physics related! Dont stop making videos! >=
As an engineering student, I won't be taking any more further studies into math past basic discrete mathematics and some basic levels of vector calculus. Your channel is there to keep me interested in the subject and act as a way to show me the true beauty behind the world of mathematics on an intuitive level. Thank you so much for your work.
"Who is your favourite mathematician?"
The answer is "Euler".
Not just Grant's answer; THE answer.
This is why he finds these kinds of questions silly...
JMUDoc Euler was a douchebag tho
That's quite a weird way to spell "Grothendieck".
Galois ftw
Ethan Alfonso - Are you sure you are not confusing him with Gauss in that regard? I’ve never read anything about Euler being a d-bag.
I like his way of analyzing things. It's always of depth and no bullshit at all.
This is certainly the pinnacle of his simulation skills.
Thank god you're usually animating -
I can't focus on anything you're saying when you look this well.
Keep on!
I though he spoke the way he does just for the voiceovers, I didn’t think it was his actual talking voice.
The way you explained Shannon's contributions and legacy was so beautiful!
Grant, my man. I've been desperately waiting for you to return to your differential equation series.
Thank you for making these complex and interesting ideas accessible!
"who's your favorite matematician"
Grant shows up.
Me: "omg that was my answer too!!"
bro's out here completing side missions
You should do something on differential forms and the Generalized Stokes' Theorem. Keep being a baller!
Thumbs up for this suggestion!
Ah yes, a "full story of Stokes'", from telescoping sums all the way up to differential forms, is one item I have on the list.
3Blue1Brown that would be awesome
@@3blue1brown plssssssss
Haha what a coincidence I just learned Stokes theorem in calc 3. It's funny what my professor told me, apparently Stokes was a professor at Cambridge and he made a problem for PhD students which was basically proving Greene's theorem in 3d
8:34 Here's a Mental health PSA/personal story.
There are three decisions in my life I regret not making sooner.
I wish I had broken up with an abusive ex earlier, I wish I had dropped out of college earlier, and I wish I had addressed my mental health earlier.
I'm now in a happy 4-year relationship, planning financially to go back to finish my degree in a year or two, and seeing a psychiatrist and therapist regularly.
It is not weak to seek help. On the contrary, it is one of the bravest things you can do.
Things will not stay bad forever. It may take a long time to realize how much progress you're making, but it will happen.
I love studying engineering and hearing " Shannon " in my control systems lectures about sampling, and then in this video 🤔 it really gives perspective
3Blue1Brown thank you so much for the work you’re doing! It is absolutely incredible!! Please do more Q&A too, it’s amazing to watch these videos!!
I marvel at your resolve to communicate mathematics in an interesting and enjoyable way. I have been a mathematician for over 30 years now, and I always take something new away from watching your videos. Thank you!
Totally agree with your point on "how to turn someone on to maths". I used to not particularly enjoy maths until I felt like I really needed them as a software developer. I finally got around to learning about vector geometry and linear algebra one day and it opened up a whole new world of possibilities for me as a programmer and I felt like it sharpened my "logical mind" if that makes sense. From then, I was hooked.
THAT'S SOOOOO TRUE!!! WHEN YOU KNOW HOW POWERFUL IT IS, HOW IT CAN TURN SOMETHING SEEMINGLY SO COMPLEX INTO SOMETHING MORE APPROACHABLE, MORE UNDERSTANDABLE, YOU CAN'T HELP FALLING FOR IT!!! WELL SAID!!
I was shocked when I saw your face, I thought you were a wise old man, who was sixty years old
I don't know if anybody ever told you that: your voice is absolutely great; it's a pleasure to listen to your videos. Which is to mean that your videos are phantastic anyway, but the sound of your voice just makes them even more enjoyable.
This guy is like the physical incarnation of math itself
I am just so irrationally proud you included the anthropocene reviewed !
Wait wait wait ......this guy doesn’t edits his voice ?
Mindbreak
You watched too many fake personality TH-camr
Yes! The Anthropocene Reviewed is fantastic!
God it's so exciting watching him explaining things. Grant is a genius. I dunno why but I burst into tears when he compares the reference material with pedagogical material. What a brilliant theory!
Finalllyyyy, waiting two days since it was ‘premiered’ was the hardest struggle ever
TLDR: necessity is the mother of invention
Being a 'Mathematician + X' has certain unique benefits which make it my preference. Being an X is important for fundamental and initial research in any area. For example, nowadays it's normal to talk about n-dimensions but the person who initially thought about representing "dimension" through a line and locating specific places on it ( points) must have started out with just one dimension in mind. The question now becomes why did they feel the need to think about the world in such a manner. This is where the X comes in. Being that X is maybe what necessitates thinking about these problems in a new way. Maybe the person being talked about was involved in trade and needed a way of measurement.
Although I agree not every example will abide by this POV but a surprising number of them will.
I genuinely enjoyed this.
Thanks 3Blue1Brown.
Be on the lookout, you might accidentally meet Veritasium
...Thank you Grant for all your time and learning tools (videos).
Don't steal Veritasium's cam-so-shaky-it'll-make-you-puke style.
It does have some shaky (it didn't bother me at all but I know what you mean) but you can just listen to it and not look at it.
This is what your normal vision would be like when you walked if it weren't for the vestibulo-ocular reflex :)
You just have to shake the opposite way and it cancels out. Try it!
Or you could try writing a software that'll detect the camera shake, and then program a mechanical stabilizer to cancel it out for you. Works every time. Try it!
@@pranavlimaye A software stabilizer that moves the browser window around to cancel out the shake. That would be fun!
I am just studying information theory for my EE degree and when you named Shannon as one of your favorite mathematicians I was so happy. I also love information theory, it is a real shame not many people know about this topic.
My favourite mathematician is only only only......YOU, Sir Grant.
you're my role model, all of your answers are thoughtful and I can learn sooo much from you
7:27 This is so real. I switched to the math major because I thought it would be the easiest major to switch to that would lead me to a job without going to grad school. Growing up, I thought math was boring and easy, but I ended up falling in love with it and will be pursuing a PhD in the fall
Applied Math. Two-year-olds or thereabouts have been watching others open and close doors and drawers by pulling and pushing on knobs and handles. For days and weeks and months they struggle to learn the secrets and perfect their processes of opening and closing doors and drawers by pulling and pushing and turning every which way on knobs and handles and changing their trials and techniques as they observe the fruits of their labor. Adults may see their efforts as play or mischief, but their brain is learning a form of applied math that only a small number of physics or engineering graduate students may study and understand. Suppose that your task is to move some object or articulating mechanism in some way using your finger(s) and/or hand(s). In a few seconds you analyze the object or mechanism and then apply your finger(s) and/or hand(s) to it in some way(s) and expect to see resulting movement(s). You evaluate the result(s) as feedback and may adjust your finger(s) and/or hand(s) input(s) to change the observed result(s). Our brains are quantifying what may be referred to as mechanism mobility associated with specific spatial directions. Suppose you want to open a closed door using a rotatable knob. Your brain believes that your hand must turn the knob left or right to release an internal latch and then your hand must pull or push on the knob in a direction perpendicular to the door's surface. Your brain believes that these may be the best directions because experience has shown that they generally offer higher mobility. Your brain is also aware of other directions of lower to zero mobility, which it believes would take much higher levels of effort to open the door, if at all. So it avoids them or may eventually try some as a last-ditch effort if all else has failed. My future applied math challenge will be to describe a numerical methodology that will provide quantitative/qualitative assessment(s) of mechanism mobility, similar to what our brains are doing with very little effort on our part.
Grant, I've learned more math and physics from your videos than I did while obtaining my m.sc.e.e. I'm eternally grateful.
Wow it's so amazing to finaly see the face behind the voice. Your explantions are very coharentic, with a great graphic demo and a calm tone. I send you from Israel my BIG FAT LIKE!
If you've never seen his face before you must have missed his appearance on numberphile recently. I'd definitly recommend checking it out
To be honest most of the math I do in game dev is linear algebra.
Ever programmed a jump?
@@moartems5076 nearly all physics in simple engines is frame-based iterative summing of the velocity and position, then some comparisons to do collision. Even computing collision time is a closed-form quadratic equation in most cases. I've seen some suggestion that partial derivates are needed to handle things like cloth simulation reasonably, because energy conservation is really important there, but otherwise the systems tend to be too dynamical for inaccuracies to matter much.
What has your experience been?
@@SimonBuchanNz There ya go, that frame based calculation is basically a time stepping scheme for an ODE. You're doing Numerical Analysis.
@@moartems5076 Eh. I see the point you're trying to make, but the actual math knowledge required is primary school level. You're probably not really doing numerical analysis here until you're doing something like computing error bounds from the exact solution, eg. to figure out physics update rate lower bounds.
@@SimonBuchanNz A lot of linear algebra in transforms, shaders, and 3D rendering as a whole.
Thanks for all you do Grant.
I think he should make more videos where he shows himself. I loved the numberphile video featuring him about the hyper-darts problem. I highly recommend it!
I honestly don't. I feel like that problem would have been presented much better in his usual style of animations and "pausing and pondering".
Thanks! That one was a lot of fun to make.
@@thedoublehelix5661 Well, maybe you're right but I really like how Brady interacts with his guest mathematicians and how he makes some appreciations that would have been averted otherwise like when he asked about what happens with the center or the perimeter.
Why is your voice so satisfying and comfortable omg
The video isn't even out and 33 people already disliked it
I guess people hate the premise of a Premiere?
I'll admit, the live chat was fun, but I would definitely not do it for a typical 3b1b video.
Sir, I really love the work you're doing. I love how you addressed the question of mental health because I've been spending a lot of time in the internet. Now I'll change my routine. Thank you so much for this Q&A. I would like you to do these kinds of videos every month. :)
In a weird way he looks like younger version of conan o'brien
Cant deny
They're both geniuses.
I was waiting for that comment
Great Grant Sir is here you can see him ..! Thanks a lot for great knowledge videos
3Blue1Brown3Dimentions
Only if you could spell right
@@avikdas4055 thx random internet person
@@AdeonWriter You're welcome, "dictionaryless" man
Articulate and thoughtful content on TH-cam makes me so happy :)
9:06 I didn't come here to be attacked so viciously. :/
What a great person you are. Thank you
I see you have adopted the Grey vlog style 😏
If I'm to understand the comments correctly, I'm somehow simultaneously stealing from Derek, Grey and Tom Scott.
@@3blue1brown Walking in the forest is the new hot thing for edutainment youtubers.
@@3blue1brown . . . and Conan, don't forget.
Love your videos, your perspective, you are doing a wonderful job
This is indeed an inconvenient time for Europe.
/me turns on coffee machine…
New way for computing eigenvectors? Every day, I learn something new :D
Man, this diff eq episode is really different from the others
"The Information" by Gleick is a masterpiece. I reread it every couple of years. Exactly how humans gained mastery (drastically decreasing entropy) by "learning" 🙂 to control information. Add a book on the evolution of RNA and metabolism (in the ocean) and the big picture comes into focus.
U aren't Tom Scott
Wait what the hell why do they look so damn similar
He also reminds me of a younger version of conan o'brien
Or is he?
Thanks for what you do.
"Modern" schooling is the reason people hate maths.
Yes. I caught the modern and antiquated used together.
Disagree! Most people are not able to grasp advanced math. They are able to learn arithmetic but many start to fail when algebra is coming up in class already. I know that i cant. Its not the teaching method.
@@Steuben1978 I don't think so, because whenever people asked questions in class the teacher would shame that person.
I was able to learn algebra with a better teacher outside of school, and Kahn academy has amazing lessons on there website.
I agree that people form put in effort to understand concepts well enough, but the school systems also promote plug and play mathematics, they don't answer why we do it a certain way, they just give formulas and you put in number and answer them
Being very good at arithmetic is not a prerequisite for maths. They are two different subjects. In fact algebra is far easier than arithmetic if it is taught correctly. Teachers are not mathematicians and generally work as teachers because they are not experts in any subject (not all of them, but most of them). That is what is wrong with schools. If you selected the best teachers, then maths teaching at schools would work. But that is not how it is done.
@@kevinmccallister7647 That does not refute my point! People differ greatly in their intellectual ability. Yes, a bad teacher or a dysfunctional family can make things worse, but for the many people who lack the necessary spatial reasoning or mathmatical ability or have bad pattern recognition....even a good teacher will not be able to make them grasp advanced math.
What an interesting perspective, on why individual authors help people to get a foothold, by explaining it 'wrong' first. This is why experts in a field have so much difficulty simplifying an introductory lecture....
_48 people went to maths prison because they _*_disliked this video_*
They were forced to solve simultaneous equations with 6 unknowns
@@JudeKennedyATCL * solve the Continuum Hypothesis within ZFC
@@badhbhchadh That's evil. Chaotic evil.
Now 71 people are in maths prison!
@Suki Desu People who don't like math should not be viewing this video. I believe that if you don't like a video on TH-cam, you should just move on. There's no need to be negative.
I can't believe I missed this. TH-cam got my priorities mixed up!
Love your channel man!
Since Terence Tao needed less than two hours to find three independent proofs of an identity about neutrino oscillations given by Stephen Parke, Xining Zhang, and Peter Denton, will they now rename the tau neutrino as Tao neutrino?